Average Error: 1.9 → 1.2
Time: 4.6s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} = -\infty:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} = -\infty:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r585115 = x;
        double r585116 = y;
        double r585117 = r585116 - r585115;
        double r585118 = z;
        double r585119 = t;
        double r585120 = r585118 / r585119;
        double r585121 = r585117 * r585120;
        double r585122 = r585115 + r585121;
        return r585122;
}
↓
double f(double x, double y, double z, double t) {
        double r585123 = z;
        double r585124 = t;
        double r585125 = r585123 / r585124;
        double r585126 = -inf.0;
        bool r585127 = r585125 <= r585126;
        double r585128 = x;
        double r585129 = y;
        double r585130 = r585129 - r585128;
        double r585131 = r585130 * r585123;
        double r585132 = r585131 / r585124;
        double r585133 = r585128 + r585132;
        double r585134 = r585130 * r585125;
        double r585135 = r585128 + r585134;
        double r585136 = r585127 ? r585133 : r585135;
        return r585136;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.9
Target2.0
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ z t) < -inf.0

    1. Initial program 64.0

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]
    2. Using strategy rm

    3. Applied associate-*r/0.3

      \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}}\]

    if -inf.0 < (/ z t)

    1. Initial program 1.2

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} = -\infty:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

  (+ x (* (- y x) (/ z t))))